In a two-electron atomic system having orbital and spin angular momenta $${l_1}{l_2}$$ and $${s_1}{s_2}$$ respectively, the coupling strengths are defined as $${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}},\,{\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}},\,{\Gamma _{{l_1}{l_2}}}$$ and $${\Gamma _{{l_2}{s_1}}}.$$ For the jj coupling. scheme to be applicable, the coupling strengths must satisfy the condition

Rithika had Rs 8000. She invested some of it in savings scheme P and the rest ofthe money in savings scheme Q. She invested for 3 years in savings scheme P and for2 years in savings scheme Q. savings scheme P offers SI at a rate of 20% pa whilesavings scheme Q compounded annually at the rate of 30% pa. The interest receivedfrom savings scheme P is 930 more than the interest received from savings scheme Q.If Rs 1500 is debited from the invested amount of savings scheme P then find thedifference between the amount invested by Rithika in savings scheme P & savingsscheme Q.

A

Rs 200

B

Rs 300

C

Rs 400

D

Rs 500

For a multi-electron atom $$l$$, L and S specify the one electron orbital angular momentum, total orbital angular momentum and total spin angular momentum respectively. The selection rules for electric dipole transition between the two electronic energy levels, specified by $$l$$, L and S are

A

ΔL = 0, ±1; ΔS = 0; Δ$$l$$ = 0, ±1

B

ΔL = 0, ±1; ΔS = 0; Δ$$l$$ = ±1

C

ΔL = 0, ±1; ΔS = ±1; Δ$$l$$ = 0, ±1

D

ΔL = 0, ±1; ΔS = ±1; Δ$$l$$ = ±1

The resonance widths $$\Gamma $$ of $$\rho ,\,\omega $$ and $$\phi $$ particle resonances satisfy the relation $${\Gamma _\rho } > {\Gamma _\omega } > {\Gamma _\phi }$$ . Their lifetimes r satisfy the relation

A

$${\tau _\rho } > {\tau _\omega } > {\tau _\phi }$$

B

$${\tau _\rho }

C

$${\tau _\rho } {\tau _\phi }$$

D

$${\tau _\rho } > {\tau _\omega }

How is the total angular momentum of a system J described in terms of spin angular momentum S and orbital angular momentum L?

A

J = L

B

J = L+S

C

J = 2πL + SBe$^{-\frac{\hbar^2}{2}}$

D

J = S2L

Deuteron in its ground state has a total angular momentum J = 1 and a positive parity. The corresponding orbital angular momentum L and spin angular momentum S combinations are

A

L = 0, S = 1 and L = 2, S = 0

B

L = 0, S = 1 and L = 1, S = 1

C

L = 0, S = 1 and L = 2, S = 1

D

L = 1, S = 1 and L = 2, S = 1

Out of the following, which are the schemes of Social Security?
(i) Provident Fund Scheme
(ii) Health Insurance Scheme
(iii) Job Guarantee Scheme
(iv) Maternity Benefit Scheme
(v) Merit Promotion Scheme
(vi) Compulsory and Voluntary Social Insurance Scheme
(vii) Child Insurance Scheme

A

(i), (ii), (iv) and (vi)

B

(ii), (i), (v) and (vii)

C

(iii), (v), (iv) and (vi)

D

(iv), (vii), (iii) and (ii)

To constitute a matter of res judicata which of the following conditions must concur?
1. The matter directly and substantially in issue in the subsequent suit or issue must be the same matter which was directly and substantially in issue either actually (section 11, explanation III) or constructively (section 11, explanation IV) in the former suit
2. The former suit must have been a suit between the same parties under whom they or any of them claim. Explanation VI of Section 11 must be read with this condition
3. The parties as aforesaid must have litigated under the same title in the former suit
4. The court which decided the former suit must have been a court competent to try the subsequent suit of the suit in which such issue has been subsequently raised. Explanation II of section 11 is to be read with condition
5. The matter directly and substantially in issue in the subsequent suit must have been heard and finally decided by the court in the first suit. Explanation V of section 11 is to be read with this condition

A

1, 2

B

3, 4

C

2, 4, 5

D

All of these

Seven people A, B, C, D, E, F and G live on separate floors of a 7-floor building. Ground floor is numbered 1, first floor is numbered. 2 and so on until the topmost floor is numbered 7. Each one of these having a different cars-Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo but not necessarily in the same order. Only three people live above the floor on which A lives. Only one person lives between A and the one having a car Cadillac. F lives immediately below the one having a car Bedford. The one having a car Bedford lives on an even-numbered floor. Only three people live between the ones having a car Cadillac and Maruti. E lives immediately above C. E is not having a car Maruti. Only two people live between B and the one having a car Fargo. The one having a car Fargo lives below the floor on which B lives. The one having a car Fiat does not live immediately above D or immediately below B. D does not live immediately above or immediately below A. G does not have a car Ambassador. Question : How many people live between the floors on which D and the one having a car Bedford ?

A

One

B

Two

C

Three

D

Four

A machine started malfunctioning due to some issues with the coupling. The coupling emplaced in the machine was Oldham. The only coupling available in the workshop is Hooke’s coupling. So Oldham coupling can be replaced by Hooke’s coupling.

A

True

B

False

A disc is a spinning with an angular velocity $$\omega $$ rad/s about the axis of spin. The couple applied to the disc causing precession will be (where $$I$$ = Mass moment of inertia of the disc and $$\omega {\text{P}}$$ = Angular velocity of precession of the axis of spin)

A

$$\frac{1}{2}I{\omega ^2}$$

B

$$I{\omega ^2}$$

C

$$\frac{1}{2}I\omega \omega {\text{P}}$$

D

$$I\omega \omega {\text{P}}$$